Momentum and Collisions: every key term you need (+ practice quiz)

More AP Physics 1 guides

• Kinematics
• Forces and Newton's Laws
• Work, Energy and Power
• Circular Motion and Gravitation
• Simple Harmonic Motion

Momentum

p = mv; property of moving object. Vector (has direction). Larger mass or velocity → more momentum.

Impulse-Momentum Theorem

Impulse = change in momentum. J = FΔt = Δp = m(v_f - v_i). Force applied over time changes momentum.

Conservation of Momentum

Total momentum before collision = total momentum after (no external forces). p_before = p_after.

Elastic Collision

Momentum and KE both conserved. Rarely real (ideal case). Example: billiard balls (approximately).

Inelastic Collision

Momentum conserved but KE lost (converted to heat, sound, deformation). Common in reality.

Perfectly Inelastic

Objects stick together after collision; maximum KE loss. Example: car crashes.

Collision Analysis

Before: p₁ + p₂ = total. After: p₁' + p₂' = total (same). Solve for unknown velocities.

Recoil

When one object pushes off another (explosion), momenta equal/opposite. Example: gun recoil when firing.

Center of Mass

Point where mass concentrated; accelerates as if all mass there. F_net = M·a_cm for whole system.

Unit 4 Summary

Momentum p=mv; impulse changes momentum. Collisions conserve momentum (elastic/inelastic). Useful for analyzing interactions.

Impulse as Area

Impulse is the area under a force-vs-time graph. A large force for a short time can deliver the same impulse as a small force for a long time, which is why airbags and crumple zones lengthen collision time.

Momentum vs Kinetic Energy

Two objects with equal momentum have KE = p²/(2m), so the lighter one carries more kinetic energy. Two objects with equal KE: the heavier one has more momentum.

Elastic Collision Special Cases (1D)

Equal masses: velocities exchange. Heavy hits light at rest: light leaves at ~2v. Light hits heavy at rest: light rebounds at ~−v, heavy barely moves.

Relative Speed Rule

In a 1D elastic collision, the relative speed of approach equals the relative speed of separation: v₁ − v₂ = −(v₁' − v₂'). This replaces the messy KE equation.

Ballistic Pendulum

Two stages: momentum conservation during the bullet's embedding (KE lost), then energy conservation as the pendulum swings up. Never apply energy conservation across the collision itself.

Explosions and Recoil

Momentum starts at zero and stays zero; fragments move so their momenta cancel. Kinetic energy is created from stored chemical or spring energy, so KE is not conserved.

2D Momentum Conservation

Conserve x- and y-momentum separately. A puck deflected at 90° in a glancing collision means the other puck carries all the original x-momentum component that was lost.

Center of Mass Motion

The center of mass of a system moves as if all external forces act on the total mass there. During an internal explosion in flight, the CM continues on the original parabola.

Choosing a System for Momentum

Momentum is conserved only if the net external force on the chosen system is zero (or the collision is so brief that external impulses are negligible). Friction with the floor over a long push breaks conservation.

Force from Continuous Impact

Water or sand hitting a surface exerts average force F = (Δm/Δt) × Δv, using the mass flow rate. Same reasoning gives thrust of a rocket.

Bounce vs Stick

A ball that bounces back experiences roughly twice the impulse of one that sticks, so it exerts about twice the average force on the wall for the same contact time.

Coefficient of Restitution (concept)

Ratio of separation speed to approach speed: 1 for perfectly elastic, 0 for perfectly inelastic. AP Physics 1 does not require the term but tests the idea through KE comparisons.

Impulse Approximation

During a brief collision, internal forces are enormous compared with weight or friction, so momentum is conserved across the collision even when the system is not otherwise isolated.

Maximum KE Loss

For given initial momenta, a perfectly inelastic collision loses the maximum possible kinetic energy consistent with momentum conservation; the remaining KE is that of the center of mass.